Electron guns generate and accelerate narrowly focused beams of electrons. In a radio frequency (RF) electron gun, the electrons are accelerated with RF energy. The transverse emittance of the electron beam refers to the electrons that travel in a direction other than along the axis of the beam. Because these electrons do not travel within the beam of the electron gun, the energy consumed in generating these electrons may be considered as wasted energy. Consequently, it is desirable to have an electron gun structure that minimizes transverse emittance.